quiddity

It's probably right to cash the ♦T first and see how they split. Assume the diamonds split 2-2. IF you are correct that half the field is in 3NT and half in 5♦, then it looks right to finesse. At the decision point, you have the possible club holdings (with normalized a priori probabilities): Qxxx x (.171) Qxx xx (.311) xxx Qx (.207) xx Qxx (.311) In the first two cases you beat +420 if you finesse, and lose to it if you drop. In the third case you lose to +400 if you finesse and beat it if you drop. In the fourth case you lose to +400 if you finesse and only tie it if you drop. There are other factors to consider, like how many of the 3NT declarers finesse vs drop, and the fact that Qx offside (drop wins) is a bit more likely than Qxxx onside (finesse wins), but I suspect if you crunch the numbers you will find that it is still a bit better to finesse. But keep in mind that a finesse here is basically a bet that a lot of the field will be in 5♦. If more people are in 3NT, or if some pairs are in clubs when a 4-1 split cannot be handled, or if some if the diamond bidders are in slam, or if some pairs miss game entirely then it quickly becomes better to play for the drop. For that reason I agree with the others, I'd probably cash out at the table without giving much thought to finessing.

This seems inconsistent to me. If bidding has much more to gain then you should be willing to go lower. The fact that you can't go lower seems to indicate that the decision is close.

I agree more with Rainer than with the people who think it's crazy. It feels close. So, not silly or excellent and probably not normal.

My disagreeing with judgment on a close call is not implying anything like that. I'm far from an expert so I could easily be wrong, but this doesn't seem (to me) like a spot where a balanced 10-count should be jumping to game. There are some minor issues with the simulation parameters - for example, opener can be 4432, responder is usually going to jump to the three-level with 5 diamonds, etc. I also think the doubler can have a slightly weaker hand - Axxx Axxx xx Qxx? Another important question is how aggressive the doubler will be in raising 3♥ to 4. I would tend to be very aggressive there; I think the jump to 3♥ shows a good invite since with a junkier 9-10 advancer perhaps can just bid 2♥ and doubler still has room to make a game try. So I think the hands with diamond voids, very good club suits etc are raises. Many of the hands with 4-card heart support are raises. I don't think it's straightforward to answer this with a simulation. A better bet would be to post a poll on bridgewinners and see how the strong players vote.

4♥ seems a bit too much on the first hand. If partner has a stiff diamond and 4-card support and 3 working controls then he can probably raise 3♥ to 4. That's not just a minimum, it's a perfect minimum.

The question of whether to take the finesse is complicated because there is an additional possible "line": some portion of the field might not get a heart lead or might just woodenly knock out the diamond and always take 11 tricks. The ruffer would beat this field when the queen ruffs out, and otherwise would tie them. The finesse would lose to the field if it loses. That field is good for the ruff and bad for the finesse. So we definitely should not finesse if it's just even money. I assume there's a point where it must be right to finesse. We could look at the case where the entire field takes the wooden line. The finesser's matchpoint expectation would be x(M) where x is the percentage of hands (among the subset which matter) where the finesse wins and M is the number of tables. The ruffer's expectation would be approximately x(M/2) + (1-x)(M). He gets half a matchpoint per table when the finesse is better and a full matchpoint per table where the ruff is better. Set these to be equal and solve for x.. x = 2/3. So if the finesse is a 2:1 favorite it looks like it must be right to finesse. So I guess the answer to "how much edge do we need" is somewhere between even money and 2:1.

[hv=pc=n&s=sak872hakt95d53c5&n=sjt964h2dkqj2c982&d=e&v=n&b=2&a=p1sp4sppp]266|200[/hv] ♥4 led to East's Jack. This is a matchpoint hand from a thread in the novice forum; I'm moving some discussion here to avoid further distraction in that thread. I found it interesting to compare the possibility of taking a third-round ruffing finesse in hearts vs trying to ruff out East's QJx. 1. E-W were robots. I assume they're probably programmed to always play the lowest of equals as third hand. If they were human, do you think restricted choice applies here or do you think humans would/should always play the jack from QJ? Is this field-dependent? 2. How much of an edge would you need to take the finesse? Again, is it field-dependent?

Thanks Ken, I think I understand now. The opening lead ♥4 excludes more of the original Qxxx possibilities than xxxx possibilities. That's a great point.

If the conditions are such that the finesse is a 2:1 favorite vs the ruff (either because of leads or restricted choice) then the two are equivalent. I will get a top 2/3 of the time. You will get a top 1/3 of the time and an average 2/3 of the time. Over the long run these have the same expectation. But in a reasonable game you won't be the only one trying to ruff out the hearts so you won't get a true top when you're right. And perhaps I won't be the only one finessing so I won't get a true zero when I'm wrong. These seem symmetric but as I mentioned in a previous post they are not. The ruffing expectation depends upon getting an average board when it's wrong. That average decays as more of the field chooses to finesse. The finesse always loses to everyone else when it's wrong, so its expectation does not decay as more of the field chooses to ruff.

Consider the cases: Qxxx Jxx xxxx QJx In both, after you play the ♥T on the third round you will have seen 3 spots from west and one honor plus one spot from east. You could always reason as you did that there are three ways for either. But if you count up the original possibilities you'll see that the first case is twice as likely as the second so the reasoning must be somehow faulty.

Field considerations. Let's assume conditions which make the finesse a favorite: no restricted choice but EW are leading 3rd/5th so it doesn't lose to East's QJxx. Then there are two heart distributions which matter: A: Qxxx Jxx (10 comb) B: xxxx QJx (5 comb) Let's assume favorable field conditions for the ruff: one table ruffs the third round, one table takes the finesse, and all other tables play on diamonds to score 11 tricks. This means that the ruff gets a near top whenever the queen falls and the finesse gets a zero when it loses to QJx. In case A, two-thirds of the cases that matter, the ruff will get a middle board and the finesse will get a top. In case B, one-third of the cases which matter, the ruffer will get a top and the finesse will get a zero. So the expectations are: ruff: .66(.5)+.33(1) = .66 finesse: .66(1)+.33(0) = .66 Equally good, but that was for the optimal field condition. As more tables try to ruff their score for case B goes down without any compensating effect, so the overall expectation for the ruff is lower. What happens if the field moves the other way and more tables try to finesse? Then the score for the finesse in case A goes down (no longer a clear top) but so does the score for the ruff (losing to more finessing tables). Also, the score for the finesse in case B goes up (no longer a clear bottom). Thus it is right to take the finesse when it is odds-on and not worry about the occasional bad board.

No takers? Here's a stab at some analysis, though I'm sure I'm missing something. Please point out any mistakes. The alternate line is a ruffing finesse against West. Draw trumps, unblocking as described, cash the second high heart pitching a club, then run the ♥T pitching another club. If LHO started with Qxxx you can now ruff out the last heart, return to hand with a trump, and pitch the last club on the fifth heart. So which line is better? The ruffing finesse gains when East started with Jxx. Initially there were 5 small heart spots outstanding, and there are 10 ways to choose 2 from those 5. It loses when East started with QJx or QJxx. There are 5 combinations of QJx and 10 combinations of QJxx. So absent any other information the ruffing finesse is a 2:3 underdog. However, there is the question of restricted choice. When East holds Jxx he must play the J at trick one, but when he holds QJx or QJxx he could theoretically play the queen instead. Perhaps the bots are programmed to always play the lower of touching honors here, in which case it doesn't apply, but if it plays an honor randomly then we should discount half of the QJx(x) holdings and the ruffing finesse now becomes a favorite. Finally there is the question of opening leads. If E-W are leading low from three or four we don't have any extra information, BUT if they are leading "3rd from even and low from 3 small" then we can do better. We lead the ♥T on the third round and check West's spot. If West's opening lead was the lowest spot then he can't possibly have Qxxx, so we would ruff. In that case we would never lose to East's QJxx, only to QJx, so the comparison would be 10 combinations of Jxx vs 5 combinations of QJx and the ruffing finesse would be a 2:1 favorite (not counting restricted choice). Similar reasoning applies if E-W are leading MUD from three small and low from Qxxx.

I don't know how severe the penalty ought to have been since I don't know the rules governing what a captain can/cannot do and I haven't seen any account describing the conversation between the captain and the tournament director. I am pretty sure that, given the state of the match, a slam swing hand was not "obviously good for the Americans" regardless of whether they were playing a strong club.

The play is not so simple; there is an alternate line which succeeds when LHO led from Qxxx. It's not obvious to me which is better Sorry, it is obvious which is better, but IMO still worth discussing both lines and how to choose between them.

Fluffy, do you think it's right to double in this spot? I wish the eurobridge site showed the auctions; I see some 3♦-x contracts but I don't know if they had the same auction.